Method and apparatus for acquiring a ranging signal of a positioning system

ABSTRACT

A method and corresponding apparatus for accurately determining the offset of the carrier frequency of a received signal from a nominal frequency (the offset due to for example Doppler shifting), such as is done in a ranging receiver when acquiring or tracking a signal transmitted by a beacon (such as a satellite) of a positioning system. The method amplifies a conventional correlation by performing a special noncoherent integration of the real and imaginary components of the output of a conventional (coherent) correlation calculation, resulting in a complex phasor having a phase that bears information about the offset of the carrier frequency from the nominal carrier frequency.

FIELD OF THE INVENTION

[0001] The present invention relates to CDMA (Code Division MultipleAccess) spread spectrum receivers, and more particularly to fastacquisition GPS (Global Positioning System) receivers (or, moregenerally, ranging receivers).

BACKGROUND OF THE INVENTION

[0002] Spread spectrum communication in its basic form is a method oftaking a data signal that is used to modulate a sinusoidal carrier andthen spreading its bandwidth to a much larger value, e.g. in a globalpositioning system (GPS) application, the spreading is achieved bymultiplying a single-frequency carrier by a high-rate binary (−1,1)pseudo-random noise (PRN) code sequence known to GPS users. Thus, thesignal that is transmitted includes a data component, a PRN component,and a (sinusoidal) carrier component.

[0003] At the receiver of such a signal, a synchronized replica of thetransmitted PRN code is required to de-spread the data sequence. Initialsynchronization, called acquisition, is followed by finesynchronization, which is called tracking.

[0004] The present invention relates primarily to acquisition, nottracking. Acquisition is the process by which the replica PRN code issynchronized (to within a small timing offset) with the code conveyed bythe received signal either for the first time or after losing apreviously acquired signal, and also by which the carrier frequency ofthe received signal is determined. Thus, to acquire a signal, anacquisition system must accurately determine any frequency-shifting ofthe received signal from the transmitted frequency in order toaccurately wipe off (remove) the carrier signal. Frequency-shifting canbe caused by relative motion of the transmitter and receiver(Doppler-shifting) as well as by clock inaccuracies (so that atransmitter and receiver sometimes do not agree on what is in fact thesame frequency). The carrier frequency-shifting results in a modulationof a code component after carrier wipe-off in the receiver. Thus, inacquiring a signal, it is also necessary that the replica code sequencebe not only time-aligned with the received code sequence, but alsomodulated to compensate for the frequency-shifting so as to fullyeliminate the PRN sequence and leave behind only the data conveyed bythe received signal. The acquisition process is therefore atwo-dimensional search, a search both in code phase and in frequency.

[0005] For some GPS signals (the civil GPS or C/A (course acquisition)code signals), the search interval in the frequency domain can be aslarge as +/−6 kHz. In addition, the phase of the received code relativeto the replica can be any possible value of code phase, due touncertainties in position of the satellite and time of transmission ofthe received signal. A PRN code period is typically 1023 chips, the termchips being used to designate bits of code conveyed by the transmittedsignal, as opposed to bits of data. Thus, the acquisition module of areceiver must search a 12 kHz-wide interval with 1023×k_(s) differentcode phases, where k. denotes the number of samples per chip.

[0006] Ordinary GPS receivers, i.e. those designed only for operationwith unobstructed satellites, search for the frequency shift with agranularity of around 1 kHz. Thus, such receivers must search12×1023×k_(s) different code/frequency combinations.

[0007] A GPS receiver designed for indoor operation must have anoperating mode with equivalent noise bandwidth on the order of 10 Hz inthe acquisition stage. Even with an equivalent noise bandwidth as smallas 10 Hz though, for reliable tracking some post-detection filteringmust still be performed as well as some further refining of the valuedetermined for the carrier frequency in the acquisition stage. Thegranularity of 10 Hz requires that the receiver search 1200×k_(s)×1023different code/frequency combinations and makes the sequential search sotime-consuming as to be unrealistic, motivating the use of parallel andfast search methods.

[0008] Because of the granularity used for the carrier frequency in theacquisition stage, the tracking stage often includes a preliminary finefrequency process for refining the carrier frequency determination,before initiating tracking. An alternative is to provide a more precisesignal acquisition, but to do so is problematic, because signalacquisition is based on performing a correlation of the received signalwith a replica, a correlation that includes an estimate of the offset ofthe carrier frequency from a nominal carrier frequency (due to theDoppler shifting and clock inaccuracies mentioned above), and since thereceived signal is modulated not only by the PRN code (for example at1.023 MHz for a coarse acquisition signal) but also by the navigationmessage at a bit rate of 50 Hz, the correlation becomes corrupted if asignal fragment is used that is longer than 20 ms (the duration of anavigation data bit). Thus there is an apparent limit of 50 Hz for theprecision with which the carrier frequency can be acquired. It ispossible to overcome the apparent limit by performing multiplecorrelations, but then signal acquisition takes longer.

[0009] What is needed is a method of fast acquisition by a GPS receiver(or, more generally, any ranging receiver, i.e. not necessarily aranging receiver used with the Global Positioning System but includingfor example ranging receivers used with GLONASS, the Russian version ofa global positioning system) that includes a more precise estimate ofthe carrier frequency than is typically provided (i.e. to within a fewHz, as opposed to 50 Hz), and so abbreviate or eliminate the need forany preliminary fine frequency process in the tracking loop of thereceiver.

SUMMARY OF THE INVENTION

[0010] Accordingly, in a first aspect of the invention, a method isprovided for determining information about the carrier frequency of asignal transmitted by a possibly moving transmitter, the signal having acode component and a carrier component, the method including: a step ofresponding to successive approximately carrier-demodulated receivedsignal fragments, and providing a set of correlation results indicatinginformation about the correlation of the approximatelycarrier-demodulated received signal fragments with a replica of the codecomponent and any remaining carrier component, wherein the set is formedusing different possible offsets from a nominal carrier frequency usedto approximately carrier-demodulate the received signal fragment, andfurther wherein each element of the set is provided as a phasor having amagnitude and a phase; and a step of responding to the set of phasors,selecting the phasor having a magnitude distinguishing it from all theother elements of the set, and determining the phase of the selectedphasor.

[0011] Further in accord with the first aspect of the invention, the setof correlation results may be a matrix of correlation results, and thematrix of correlation results may be spanned by an index indicating anoffset from a nominal carrier frequency and also by an index indicatingcode phase, and the selected phasor may be the phasor having the maximummagnitude of all the elements of the set. Further, the step of providingthe matrix of correlation results may include a step of performing acoherent integration of each of a series of signal fragments, and a stepof performing a non-coherent integration in which the phasor results ofthe coherent integrations are combined without regard to phase. Furtherstill, the step of performing the non-coherent integration may involvemultiplying each element of a matrix of correlation results providedusing a coherent integration of a first signal fragment, by the complexconjugate of a corresponding element for an immediately preceding signalfragment. Also further, in providing the matrix of correlation resultsas phasor values and in determining the phase of the phasor having themaximum magnitude of all the elements of the matrix, in someapplications only at most two phasor values may be held in a memorydevice at any instant of time, and of the two phasor values, only thephasor value having the larger magnitude may be saved in the memorydevice before calculating a next phasor value.

[0012] In a second aspect of the invention, an apparatus is provided fordetermining information about the carrier frequency of a signaltransmitted by a possibly moving transmitter, the signal having a codecomponent and a carrier component, the apparatus including: means,responsive to approximately carrier-demodulated received signalfragments, for providing a set of correlation results indicatinginformation about the correlation of the approximatelycarrier-demodulated received signal fragments with a replica of the codecomponent and any remaining carrier component, wherein the set is formedusing different possible offsets from a nominal carrier frequency usedto approximately carrier-demodulate the received signal fragment, andfurther wherein each element of the set is provided as a phasor having aphase and a magnitude; and means, responsive to the set of phasors, forselecting the phasor having a magnitude distinguishing it from all theother elements of the set, and determining the phase of the selectedphasor, and for providing information about the carrier frequency basedon the phase of the selected phasor.

[0013] Further in accord with the second aspect of the invention, theset of correlation results (phasors) may be a matrix of correlationresults, and further wherein the matrix of correlation results may bespanned by an index indicating an offset from a nominal carrierfrequency and also by an index indicating code phase, and wherein theselected phasor may be the phasor having the maximum magnitude of allthe elements of the set. Further, the means for providing the matrix ofcorrelation results may include means, responsive to a series of signalfragments, for performing a coherent integration of each of the seriesof signal fragments, and also means, responsive to the coherentintegrations, for providing a non-coherent integration in which thephasor results of the coherent integrations are combined without regardto phase. Still further, the means for performing the non-coherentintegration may multiply each element of a matrix of correlation resultsprovided using a coherent integration of a first signal fragment, by thecomplex conjugate of a corresponding element for an immediatelypreceding signal fragment. Also further, in some applications, inproviding the matrix of correlation results as phasor values and indetermining the phase of the phasor having the maximum magnitude of allthe elements of the matrix, only at most two phasor values may be heldin a memory device at any instant of time, and of the two phasor values,only the phasor value having the larger magnitude may be saved in thememory device before calculating a next phasor value.

[0014] In a third aspect of the invention, a system is providedincluding: a transmitter for transmitting a signal having a codecomponent and a carrier component, and a ranging receiver for receivingthe signal and for determining information about the carrier frequencyof the signal, the ranging receiver characterized in that it includes:means, responsive to approximately carrier-demodulated received signalfragment, for providing a set of correlation results indicatinginformation about the correlation of the approximatelycarrier-demodulated received signal fragments with a replica of the codecomponent and any remaining carrier component, wherein the set is formedusing different possible offsets from a nominal carrier frequency usedto approximately carrier-demodulate the received signal fragment, andfurther wherein each element of the set is provided as a phasor having aphase and a magnitude; and means, responsive to the matrix of phasors,for selecting the phasor having a magnitude distinguishing it from allthe other elements of the set, and determining the phase of the selectedphasor, and for providing information about the carrier frequency basedon the phase of the selected phasor.

[0015] Further in accord with the third aspect of the invention, thesystem provided by the invention may also include a computing resourceexternal to the ranging receiver, and the apparatus may communicateinformation to the computing facility via a wireless communicationsystem and the computing facility may provide at least some of thecomputation needed either to provide the set of correlation results orto select the phasor.

[0016] The invention provides fine frequency estimates of the carrierfrequency used to convey ranging signals immediately after initialacquisition; such estimates can be used for tracking or as theinitialization of more sensitive dine acquisition algorithm, and sosimplifying the search for the carrier frequency. The invention thusallows removing a fine acquisition stage from a ranging receiver, savingin some embodiments for example as much as one or two seconds foracquisition in typical ranging receivers, or simplifying the operationof such a stage, reducing the computational burden in some embodimentsfor example by as much as a factor of up to fifty.

BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The above and other objects, features and advantages of theinvention will become apparent from a consideration of the subsequentdetailed description presented in connection with accompanying drawings,in which:

[0018]FIG. 1 is a flowchart of the invention;

[0019]FIG. 2 is a block diagram/flow diagram of a GPS receiver in whichthe invention can be implemented; and

[0020]FIG. 3 is a block diagram/flow diagram of an apparatus thatimplements the invention.

BEST MODE FOR CARRYING OUT THE INVENTION

[0021] The invention is described below as a subprocess of theacquisition stage of a ranging receiver such as a GPS receiver and whenspecific numerical examples are given, civil GPS signals (C/A codesignals) are used, but it should be understood that the invention can beused in any receiver of a spread spectrum signal, not necessarilyreceivers used to provide navigation solutions, and the invention is ofcourse not restricted to use with civil GPS (C/A code) signals. Theinvention provides a relatively precise estimate of the offset of thecarrier frequency from a nominal carrier frequency, the offsetattributable to one or another of various causes including Dopplershifting or clock inaccuracies (the clock of either the ranging receiveror the clock of the source of the spread spectrum signal, i.e. asatellite in case of a GPS receiver). The invention achieves its objectby performing, as part of the processing of the acquisition stage, amodified correlation (modified as compared to the correlation performedin prior art ranging receivers) of a received signal fragment with areplica of the PRN code known to be used by the source of the signal.

[0022] As explained above, the acquisition process determines the codephase (the relative phase of the replica and the received signalfragment) and also the frequency of any complex sinusoidal modulationremaining after carrier wipeoff assuming a nominal carrier frequency,i.e. it also determines a remaining frequency offset from the nominalcarrier frequency.

[0023] The code phase is determined according to the peak of acorrelation function. As explained above, the length of the receivedsignal fragment used in performing the correlation is, according to theprior art, restricted typically to 20 ms because modulation of thereceived signal fragment by the 50 Hz navigation data corrupts anordinary correlation using a longer signal fragment.

[0024] A process according to the present invention for arriving at amore precise estimate of the remaining frequency offset Δf (from anominal carrier frequency f₀) begins with a signal fragment after bothcode wipeoff and nominal carrier frequency demodulation by each coarsefrequency. The description that follows will use equations (1)-(6) thatare valid only after demodulation by the correct code phase and also bythe correct coarse frequency, i.e. the code phase and coarse frequencyoffset for which a process of coherent and non-coherent integrations inperforming a correlation of the signal fragment with a code replica anda carrier replica (i.e. a sinusoid at a frequency equal to the coarsefrequency offset), as described below, gives the largest correlationresult. For other code phase and coarse frequency pairs, more generalequations apply, equations that reduce to equations (1)-(6) for thecorrect code phase and coarse frequency pair.

[0025] For purposes of the present invention, the signal fragment can bemodeled as,

x(n)=a _(n) e ^(2πjΔfnΔt) +x _(noise)(n)=a _(n) e ^(2πj(Δf) ^(_(c))^(+Δf) ^(_(f)) ^()nΔt) +x _(noise)(n)  (1)

[0026] where the remaining frequency offset Δf is presented as acombination of a coarse frequency offset Δf_(c) with some granularityΔf_(c,step) (e.g. 100 Hz) and a fine frequency offset Δf_(f), which ispreferably in the range (−Δf_(c,step)/2, +Δf_(c,step)/2). The codewipe-off in the context of the present invention is to be understood asthe multiplication of the signal fragment by the replica code withoutintegration. If the code phase is correct then the code is wiped off andonly modulations due to navigation data bits and residual Dopplerremain. If the coarse frequency offset guess during the acquisitionprocess is correct, then the correlation peak will be found and the finefrequency offset Δf_(f) can be estimated.

[0027] In the following description of the invention, the noisecomponent x_(noise)(n) is omitted for clarity. Moreover, the amplitudea_(n) in eq. (1) should be understood to be the amplitude of the signalfragment x(n), i.e. the amplitude of the signal after code wipeoff usingthe correct code phase, and after frequency demodulation using asuitably good estimate of the coarse frequency offset Δf_(c) (a goodestimate in that it is substantially the best guess possible using astep size of 50 Hz). If the estimate of the coarse frequency offsetyields a frequency that is far from the true carrier frequency(including the Doppler, etc.) or if the code phase is not correct, thenthe signal value x(n) is small, i.e. it is suppressed. The descriptionthat follows does not address such cases. The problem addressed by theinvention is to find a fine frequency offset after the acquisitionsearch determines the correct code phase (i.e. code wipeoff is assumed)and some coarse frequency estimate (so that the signal arriving at alogic module implementing the invention is assumed demodulated by theestimated coarse frequency). Of course in actual practice, the inputs toa logic module that implements the invention will be a number ofdifferent correlations, each based on a coherent integration of thereceived signal fragment with a particular code phase and a particularcoarse frequency offset.

[0028] The integration (summation) of an ordinary correlationcalculation subsamples and thereby enhances the signal component, eachsubsample corresponding to a different increment of Δf_(f), i.e. Δf_(f),2Δf_(f), 3Δf_(f), . . . , N_(c)Δf_(f), where N_(c) is the number ofincrements of Δf_(f) included in the ordinary correlation. Afterdemodulation by the factor e^(−2πjf) ^(_(c)) ^(nΔt) to account for thecoarse frequency offset, each subsample indicated by the indexn=n₁N_(c)+n₂, can be expressed as, $\begin{matrix}{{{y\left( n_{1} \right)} = {{\underset{n_{2} = 0}{\sum\limits^{N_{c} - 1}}{a_{{n_{1}N_{c}} + n_{2}}^{2\quad \pi \quad {j{({{\Delta \quad f_{c}} + {\Delta \quad f_{f}}})}}{({{n_{1}N_{c}} + n_{2}})}\Delta \quad t}^{{- 2}\quad {\pi j}\quad \Delta \quad {f_{c}{({{n_{1}N_{c}} + n_{2}})}}\Delta \quad t}}} \approx {{\overset{\sim}{a}}_{n_{1}}^{2\quad \pi \quad {j\Delta}\quad f_{f}n_{1}N_{c}\Delta \quad t}}}},} & (2)\end{matrix}$

[0029] where N_(c) is the number of samples in the coherent integration(indicated by eq. (2)) and is usually some integral multiple of the PRNcode epoch. The result, y(n₁), is the (integrated) signal at a discretetime indicated by n₁; y(n₁) is, more specifically, a fragment of thereceived, code-wiped signal, N_(c) samples long, correlated with thesinusoid e^(−2πjΔf) ^(_(c)) ^((n) ^(₁) ^(N) ^(_(c)) ^(+n) ^(₂) ^()Δt).(The index n is used to indicate an instant of time before the coherentintegration, with n incrementing with each new sample. For example, ifthere are two samples per chip then the sampling rate is 2*1,023,000samples per second, and so n increments 2*1,023,000 for each second.)After the coherent integration, which is an integration over an integralmultiple of the code epoch length (i.e. an interval of length k*1023chips for some integer k), a second time index n₁ is used, one thatincrements every coherent integration length. For example, if thecoherent integration length is just one code epoch (i.e. 1023 chips),then the integrated sampling rate will be 1000 samples per second; i.e.with the coherent integration, every 1023 samples are accumulated into asingle, integrated sample.

[0030] Bear in mind that, as mentioned above, in actual practice thequantity y(n₁) is calculated for a particular code phase and aparticular coarse frequency offset. If the code phase is indicated by anindex p and the coarse frequency is indicated by an index m, then y(n₁)is more properly written as y_(p,m)(n₁), but for simplicity of notation,the p,m dependence is suppressed in what follows.

[0031] Multiplying each sample after the coherent processing, given byeq. (2), by the complex conjugate of the nearest neighbor sampleoccurring earlier in time, provides,

z(n ₁)≡y(n ₁)y ^(*)(n ₁−1)=ã _(n) ₁ ã _(n) ₁ ₊₁ e ^(2πjΔf) ^(_(f)) ^(n)^(₁) ^(N) ^(_(c)) ^(Δt) e ^(−2πjΔf) ^(_(f)) ^((n) ^(₁) ^(−1)N) ^(_(c))^(Δt) =ã _(n) ₁ ã _(n) ₁ ₊₁ e ^(2πjΔf) ^(_(f)) ^(N) ^(_(c)) ^(Δt)  (3)

[0032] which compensates for the time (code epoch) dependence n₁.Defining {tilde over ({tilde over (a)})}_(n) ₁ ≡ã_(n) ₁ ã_(n) ₁ ₊₁, andusing the well-known Euler's theorem, the quantity z(n₁) can be writtenas,

z(n ₁)={tilde over ({tilde over (a)})}_(n) ₁ e ^(2πjΔf) ^(_(f)) ^(N)^(_(c)) ^(Δt) ={tilde over ({tilde over (a)})} _(n) ₁ [cos(2πΔf _(f) N_(c) Δt)+j sin(2πΔf _(f) N _(c) Δt)].  (4)

[0033] The amplitude {tilde over ({tilde over (a)})}_(n) ₁ of thesinusoidal quantity z(n₁) in general can vary with time (since itdepends on n₁, which indicates an instant of time), due to the BPSK datamodulation, while the other terms of the quantity z(n₁) (the terms insquare brackets in eq. (4) yielding the phase of the phasor quantityz(n₁)) do not depend on time. And here is the key to understanding theinvention: one can find the phase of the phasor quantity z(n₁) easilyenough because that phase does not change with time, and since thatphase has information about the sought-after fine frequency offsetΔf_(f), we can use the phase to find the fine frequency offset Δf_(f).

[0034] Now, according to the invention, a more precise estimate of thefrequency offset than results from an ordinary correlation is providedby what is here called a (supplemental) non-coherent processing stagethat integrates (sums) the absolute values of real part of the signalz(n₁) for different times each indicated by a different value of n₁,and, separately, the imaginary parts, as follows: $\begin{matrix}{{c^{(r)} \equiv {\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{{Re}\left( {z\left( n_{nc} \right)} \right)}}}} = {\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{{\overset{\overset{\sim}{\sim}}{a}}_{n_{nc}}{\cos \left( {2\quad \pi \quad \Delta \quad {fN}_{c}\quad \Delta \quad t} \right)}{ = }{\cos \left( {2\pi \quad \Delta \quad {fN}_{c}\Delta \quad t} \right)}{{{\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{\overset{\overset{\sim}{\sim}}{a}}_{n_{nc}}}},\text{and}}\quad}}}}} & (5) \\{{c^{(i)} \equiv {\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{{Im}\left( {z\left( n_{nc} \right)} \right)}}}} = {\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{{\overset{\overset{\sim}{\sim}}{a}}_{n_{nc}}{\sin \left( {2\quad \pi \quad \Delta \quad {fN}_{c}\quad \Delta \quad t} \right)}{ = }{\sin \left( {2\pi \quad \Delta \quad {fN}_{c}\Delta \quad t} \right)}{{{\underset{n_{nc} = 0}{\sum\limits^{N_{nc} - 1}}{{\overset{\overset{\sim}{\sim}}{a}}_{n_{nc}}}},}}}}}} & (6)\end{matrix}$

[0035] where N_(nc) is the number of integrated samples in thenoncoherent integration, i.e. the noncoherent integration length. Thevalue used for N_(nc) depends on the signal strength; it is smaller fora higher signal strength, and could even be as small as one.

[0036] As explained above, the amplitude a_(n) and so the amplitudeã_(n) ₁ and likewise the amplitude {tilde over ({tilde over (a)})}_(n) ₁are amplitudes for a particular code phase p and a particular frequencyoffset m, both p and m being integers and serving as indices, but theindices p and m are suppressed in eqs. (1)-(6) above for clarity ofnotation. Thus, the amplitude {tilde over ({tilde over (a)})}_(n) ₁ isreally shorthand for {tilde over ({tilde over (a)})}_(n) ₁ _(,p,m) wherethe index n₁ refers to a particular code epoch (and so to a particularinstant of time). Thus also z(n₁) is shorthand for z_(p,m)(n₁), and soc^((r)) is shorthand for c_(p,m) ^((r)) and similarly for c^((i)).

[0037] Now according further to the invention, after performing the twonon-coherent integrations given by eqs. (5) and (6), and constructingthe matrix c_(p,m) according to,

c _(p,m) =c _(p,m) ^((r)) +jc _(p,m) ^((i))  (7)

[0038] (now again making express the p,m dependence of c_(p,m) ^((r))and c_(p,m) ^((i)) of eqs. (5) and (6)), the set of all |c _(p,m) |=|c_(p,m) ^((r)) +jc _(p,m) ^((i))|={square root}{square root over ((c_(p,m) ^((r)))²+(c _(p,m) ^((i)))²)}  (8)

[0039] is searched to find which is the maximum, indicated here as$\max\limits_{p,m}{\left\{ {c_{p,m}} \right\}.}$

[0040] The indices p and m for which |c_(p,m)| attains its maximumindicate the code phase and coarse frequency offset. According to theinvention, the real component c_(p,m) ^((r)) with p,m for which|c_(p,m)| attains its maximum, and the corresponding imaginary componentc_(p,m) ^((i)) are then used to determine the fine frequency offsetΔf_(f) on the basis that these two quantities indicate the phase of aphasor c_(p,m)=c_(p,m) ^((r))+jc_(p,m) ^((i)) (for the best p,m, i.e.for the p,m for which |c_(p,m)| attains its maximum), a phase thatdepends on the fine frequency offset Δf_(f).

[0041] Thus, at each pair of values of frequency and code phase thatwould be searched in a conventional acquisition, the invention providesnot one correlation output (including coherent and noncoherent part),but two outputs, c_(p,m) ^((r)) and c_(p,m) ^((i)). The strength of theresponse is calculated using the sum of the squared values of the twooutputs, and the peak in the strength so calculated corresponds to thecorrect frequency and code phase pair. But in addition, the two outputsc_(p,m) ^((r)) and c_(p,m) ^((i)) give information useful in determininga fine frequency offset, i.e. a frequency offset fine enough to estimatethe carrier frequency to within better than 50 Hz. (After the coherentintegration, we do have complex correlation values and in principle itis possible to obtain a fine frequency offset directly from the outputof the coherent integration, but in practice, in weak signal conditions,it is necessary to essentially amplify the correlation result using thenon-coherent integration process of the invention. As mentioned above, alonger-interval coherent integration will not work well because of themodulation of the received signal by the navigation data.)

[0042] In summary, in a conventional noncoherent integration process,inputs x(n) (correlations of signal fragments after code wipeoff andcoarse acquisition) are complex numbers a_(n)+jb_(n) (more properlya_(n,p,m)+jb_(n,p,m), but the indices p and m, indicating code phase andfrequency offset respectively, are dropped here for simplicity ofnotation), and noncoherent integration is performed (in a calculation toamplify the correlation of the signal fragment with a signal of each ofseveral different code phases and each of several different frequencyoffsets) as an integration of absolute values |a_(n)+jb_(n)| or squaredvalues |a_(n)+jb_(n)|². In the present invention, in contrast,noncoherent integration is performed by: first, multiplying each inputby the complex conjugate of its neighbor, i.e. forming the product(a_(n)+jb_(n))·(a_(n−1)−jb_(n−1)); and second, noncoherentlyintegrating, separately, the imaginary part (b_(n)a_(n−1)−a_(n)b_(n−1))and the real part (a_(n)a_(n−1)+b_(n)b_(n−1)). The result is two values(c^((r)),c^((i))) (actually (c_(p,m) ^((r)),c_(p,m) ^((i))), but thedependence on the code phase index p and frequency offset index m aredropped for simplicity of notation) for the correlation at eachfrequency and code phase pair of the search. The largest of the sum ofthe squares of c^((r)) and c^((i)) (or the square root thereof) is usedto determine the fine frequency offset, based on the phase of the phasorc^((r))+jc^((i)). The fine frequency offset so determined, when combinedwith the coarse frequency offset (determined as in the prior art to aprecision of for example +/−50 Hz) and with the nominal frequency,yields a precise value (for example, to within 1-2 Hz) for the carrierfrequency (including Doppler and other deviations from the nominalcarrier frequency).

[0043] Eqs. (5) and (6) allow only an ambiguous determination of thefine frequency offset Δf_(f); for a properly designed acquisition system(i.e. having a proper choice of frequency spacing), four solutions arepossible: $\begin{matrix}{{{\Delta \quad f_{f,1}} = \frac{{arc}\quad {{tg}\left( {c^{(i)}/c^{(r)}} \right)}}{2\quad \pi \quad N_{c}\Delta \quad t}},} & (9) \\{{{\Delta \quad f_{f,2}} = {- \frac{{arc}\quad {{tg}\left( {c^{(i)}/c^{(r)}} \right)}}{2\quad \pi \quad N_{c}\Delta \quad t}}},} & (10) \\{{{\Delta \quad f_{f,3}} = {\pi \quad - \frac{{arc}\quad {{tg}\left( {c^{(i)}/c^{(r)}} \right)}}{2\quad \pi \quad N_{c}\Delta \quad t}}},{and}} & (11) \\{{\Delta \quad f_{f,4}} = {{- \pi} + {\frac{{arc}\quad {{tg}\left( {c^{(i)}/c^{(r)}} \right)}}{2\quad \pi \quad N_{c}\Delta \quad t}.}}} & (12)\end{matrix}$

[0044] where c^((r)) is shorthand for c_(p,m) ^((r)) for the p,m forwhich |c_(p,m)=c_(p,m) ^((r))+jc_(p,m) ^((i))| (or, equivalently,|c_(p,m)|²) is maximum, and similarly for c^((i)).

[0045] The estimate of the fine frequency offset is ambiguous (havingthe four possible results given by eqs. (9)-(12)) because of takingabsolute values of imaginary and real components. Nonetheless, theuncertainty in the fine frequency offset is greatly reduced using theinvention. The ambiguity can be resolved by one or another methodexecuted by the acquisition stage prior to handoff to the trackingalgorithm, or the tracking algorithm can be initiated with all fourpossible solutions as input.

[0046] Referring now to FIG. 1, a flowchart of the invention is shown asbeginning with a first step 11 in which a received signal fragment x(n),at a time indicated by the variable n, is correlated with a replica codeat a number of different code phases indicated by index p and alsocorrelated with (in effect) a number of different replica carriersinusoids, each including a different coarse frequency offset indicatedby index m, producing an output y_(p,m)(n₁) for each different codephase and coarse frequency offset, the index n₁ incrementing over everyN_(c) samples, whereas the original index n increments with each sample.Next, in a step 12, each y_(p,m)(n₁) is multiplied by the complexconjugate of its neighbor, i.e. by y_(p,m) ^(*)(n₁−1), producingz_(p,m)(n₁) having real and imaginary components, for all different p,m.Next, in a step 13, the real and imaginary components of the quantitiesz_(p,m)(n₁) for all p,m are each (separately) noncoherently integratedover N_(nc) values of n₁ (each value of n₁ corresponding to N_(c)samples), as indicated by eqs. (5) and (6). The result is a quantityc_(p,m) having real and imaginary components c_(p,m) ^((r)) and c_(p,m)^((i)) respectively. Next, in a step 14, the c_(p,m) are searched overall p,m to find the p,m for which |c_(p,m)| (or, equivalently,|c_(p,m)|²) is a maximum, yielding a “best” p,m and correspondingc_(p,m) ^((r)) and c_(p,m) ^((i)). Finally, in a step 15, (ambiguous)information about the fine frequency offset Δf_(f) is determined basedon the ratio c_(p,m) ^((i))/c_(p,m) ^((r)), as set out in eqs. (9)-(12).As explained above, the ambiguity in the fine frequency offset can beresolved by further processing within the acquisition module, or theambiguous information can be provided to the tracking module and theambiguity can be resolved there.

[0047] Still referring to FIG. 1, in essence the method includes a firststep 100, including substeps 11, 12, and 13, which provides a matrix 104of correlation results indicating information about the correlations ofthe approximately carrier-demodulated successively received signalfragments 102 with a replica of the code component and a replica of anyremaining carrier component (i.e. a sinusoid having a frequency equal toa coarse offset from the nominal carrier frequency), wherein the matrixis spanned by the index p indicating code phase and the index mindicating an offset from a nominal carrier frequency used toapproximately carrier-demodulate the received signal fragments, andfurther wherein each element of the matrix 104 is provided as a phasor(c_(p,m)); and a second step 104 of responding to the matrix 104 ofphasors and determining the phase of the phasor having the maximummagnitude of all the elements of the matrix, and so providing a moreprecise value for the carrier frequency of the carrier than what isprovided by the offset for the phasor having the maximum magnitude.

[0048] Referring now to FIG. 2, an exemplary embodiment of a rangingreceiver 20 in which the invention can be implemented is shown receivinga signal s(t) corresponding to a transmitted signal s_(t)(t), given by,

s _(t)(t)=AC(t)P(t)cos(wt).

[0049] The receiver 20 includes an acquirer 21 (in which logic codeimplementing the steps of the invention as indicated in FIG. 1 ishosted) for acquiring the signal, and a tracking module 24 for makingadjustments necessary to track the acquired signal, i.e. the maintainacquisition. The received signal s(t) includes a code component C_(φ)(t)at a phase φ relative to the phase of the code component of thetransmitted signal, a carrier component A×cos(w′t+φ_(car)) the φ_(car)indicating that the carrier component of the received signal is out ofphase by an amount φ_(car) with respect to the transmitted signal, and adata component P(t), again in general differing in phase from the datacomponent of the transmitted signal although not expressly indicated.The carrier frequency w′ is different than the transmitted frequency w(w′ is shifted in frequency from the nominal carrier frequency w)because of the relative motion of the transmitter and receiver, i.e.because of Doppler shifting, and also because of inaccuracies in thereceiver and transmitter clocks. A replica of the code componentC_(φ)(t) is generated in the receiver (in either the acquirer 21 or thetracking module 24, depending on the stage of operation) with some phaseφ. In routine receiver operation, after the receiver has acquired asignal, in order to extract the data component the receiver mixes thereceived signal with a sinusoid at a received carrier frequency w′, andalso mixes the signal with a replica code C_(φ)(t) at a replica codephase φ that puts the replica code in phase with the transmitted code.(The phases are different because of the transmission time from thesatellite to the receiver and also because the clocks in the receiverand transmitter are not synchronized.)

[0050] The received carrier frequency w′ and the correct replica codephase y are determined by an acquirer 21. To acquire the signal s(t),and so to determine the received carrier frequency w′ and replica codephase φ, the receiver provides a portion of the received signal s(t) toa radio-frequency (RF) to baseband module that includes an RFdownconverter and an analog-to-digital converter (ADC), providing anapproximately baseband signal s′(n) (the index n indicating a samplemade at a particular time and so indicating the particular time), whichstill includes the code component C(n). The RF to baseband moduleprovides in-phase and quadrature versions of the received, downconvertedsignal, and provides the two versions to respective ADC modules. One ADCmodule then provides an in-phase digitized, downconverted receivedsignal s′_(I)(n), and the other provides a quadrature digitized,downconverted signal s′_(Q)(n). The combination of two such outputs istreated as a complex entity in what follows.

[0051] Instead of an RF to baseband down-converting followed by ananalog to digital conversion, it is also possible to use an RF tointermediate frequency conversion followed by a conversion to basebandcombined with ADC.

[0052] Once the acquirer 21 precisely determines the carrier frequencyw′, including any shifting δw away from the nominal carrier frequency w,and also the replica code phase φ, the receiver 20 can extract the datasignal P(t) from the received signal s(t) by for example first mixingthe received signal s(t) with a sinusoid at the precisely determinedcarrier frequency w′, then mixing the resulting signal with asynchronized (in phase) replica code signal C_(φ)(t), and finallyperforming an integrate and dump, leaving only the data signal P(t).Sometimes the data extraction is performed within the tracking module24, as is indicated in the embodiment shown in FIG. 2. The trackingmodule then not only extracts the data signal P(t) but also examines itto determine whether to make slight, tracking adjustments to the carrierfrequency w′ or the replica code phase T so as to keep the receiver 20tuned to the signal s(t).

[0053] Still referring to FIG. 2, the signal s′(n), referring to boths′_(I)(n) and s′_(Q)(n), includes both a code component C(n) as well asa residual carrier component depending on the shift δw. As explainedabove, the shift δw in some applications is typically anywhere in abandwidth of 12 kHz about the nominal carrier frequency w. The code C(n)is typically a pseudorandom sequence of bits of a predetermined length.In case of civil GPS applications, a code-length of 1023 bits is used.Since the code does not itself convey information and is instead merelya device by which the bandwidth of an information-bearing signal isspread over a much wider bandwidth in a way that allows otherinformation-bearing signals to also be spread over and use the samebandwidth, a bit of such a code is referred to as a chip, instead of abit. The chip rate is typically much greater than the bit rate of theinformation-bearing signal P(n). In GPS applications, the chip rate istypically 1023 chips per millisecond, whereas the data P(n) is nominally50 bits per second.

[0054] Still referring to FIG. 2, the acquirer 21 is shown as includinga coarse carrier wipeoff module (CCWM) 22 including a numericallycontrolled oscillator (NCO), a processing module 23 (hosting the codelogic for practicing the invention), a control module, a scanningmodule, and switching modules used to switch from acquiring to trackingafter a signal is satisfactorily acquired. The control module operatesthe switches SW1 and SW2 so that once the signal has been acquired (withrespect to both carrier frequency and code phase), the acquisitionmodule is switched out of the circuit including the NCO, and thetracking module 24 is switched into that circuit.

[0055] The approximate baseband signal s′(n) is provided to the CCWM 22,which mixes s′(n) with a complex sinusoid (i.e. an in-phase andquadrature sinusoid are mixed with the in-phase and quadratureapproximate baseband signals s′_(I)(n) and s′_(Q)(n)), at one of anumber of several distinct frequencies in a set of coarse frequencyoffsets spanning a range of frequencies about the nominal frequencyencompassing all possible frequency shifts. For example, in the case ofa GPS receiver, the CCWM 22 would first mix the input s′(n) with asignal at 6 kHz below the nominal carrier frequency, to provide x(n).Later, at the command of the analysis module 23 d, the CCWM 22 would mixthe same signal s′(n) at a next coarse frequency, 5 kHz below thenominal carrier frequency, and so on, each time producing a differentsignal (complex) x(n) including a different coarse frequency component.

[0056] As will be explained below and as mentioned above, the processingmodule 23 includes components for performing the steps indicated inFIG. 1. The output of the processing module, which is used as the inputto the tracking module 24, is preferably an unambiguously determinedcarrier frequency w′ and a code phase φ.

[0057] Note that according to the invention, a carrier wipeoff usingeach of the coarse frequencies is needed by the processing module 23before the processing module can begin the analysis used to acquire asignal. Thus, the processing module does not pass control to thetracking module 24 until after having the CCWM 22 perform an approximatecarrier wipeoff with each coarse frequency spanning a range offrequencies presumed to include the actual to-be-determined carrierfrequency, and then performing the analysis used to indicate a precisevalue for the carrier frequency according to the steps indicated inFIG. 1. In the course of performing the analysis, as explained above,the phasors c_(p,m) corresponding to the different coarse frequenciesare constructed and that having the largest magnitude is determined. Tofind the c_(p,m) for which |c_(p,m)| is a maximum, either each c_(p,m)can be saved and the resulting array of c_(p,m) searched after allc_(p,m) are constructed, or instead only the c_(p,m) for which |c_(p,m)|is so far the maximum can be saved.

[0058] Referring now to FIG. 3 and also to FIG. 1, the processing module23 of FIG. 2 is shown in more detail as including modules implementingthe steps indicated in FIG. 1. A module 31 (FIG. 3) performs thecoherent integration of step 11 (FIG. 1), storing the results of eachcoherent integration for a particular code phase (indicated by an indexp) and coarse frequency offset (indicated by an index m) in a memorydevice 31 a. When all of the coherent calculations are completed (i.e.for all p and all m, the range in p and m sufficient to span allpossible code phases and all possible carrier frequency shifts), aneighbor multiplication module 32 then performs the neighbormultiplication step 12. Next, a non-coherent integration module 33performs the non-coherent integration step 13, amplifying the results ofthe coherent integration. A single matrix of results (each results beinga complex number) is provided as an output of the non-coherentintegration module 33; the matrix is spanned by the code phase index pand the coarse carrier frequency index m. A maximum finder module 34then searches the matrix and finds the p and m for which the magnitudeof the complex matrix elements is a maximum (or, equivalently, thesquare of the magnitude). Finally, a solver module 34 determines thephase of the phasor corresponding to the complex elements for the foundp and m, extracts information about the fine frequency offset (accordingto step 14), and, in the preferred embodiment, performs furtherprocessing to eliminate the ambiguity of the results described inconnection with eqs. (9)-(12). The output of the solver module istherefore, in the preferred embodiment, the precisely determined carrierfrequency (including both the coarse and fine frequency offsets) andalso the code phase, both of which are then used by the tracking phaseof the receiver.

[0059] Still referring to FIG. 3, from another perspective, theinvention is in essence an apparatus including: a first module 300,responsive to successive approximately carrier-demodulated receivedsignal fragments 302, for providing a matrix 304 of correlation resultsindicating information about the correlation of the approximatelycarrier-demodulated received signal fragment with a replica of the codecomponent and a replica of any remaining carrier component, wherein thematrix is spanned by an index p indicating code phase and an index mindicating a first offset from a nominal carrier frequency used toapproximately carrier-demodulate the received signal fragment, andfurther wherein each element of the matrix is provided as a phasorc_(p,m) having a phase and a magnitude; and a second module 306,responsive to the matrix of phasors 304, for determining the phase ofthe phasor having the maximum magnitude of all the elements of thematrix, and for providing information about the carrier frequency basedon the phase of the phasor having the maximum magnitude of all theelements of the matrix. In the preferred embodiment, the first module300 includes: a first sub-module 31, responsive to a series of signalfragments, for performing a coherent integration of each of the seriesof signal fragments, preferably by multiplying each element of a matrixof correlation results provided using a coherent integration of a firstsignal fragment, by the complex conjugate of a corresponding element foran immediately preceding signal fragment; and also a second sub-module32, responsive to the coherent integrations, for providing anon-coherent integration in which the phasor results of the coherentintegrations are combined without regard to phase.

[0060] It should be understood that the in performing the neighbormultiplications for forming the noncoherent sums, although the inventionhas been described above in which neighbor multiplications aremultiplications of the first and second coherent integration result,then the second and third, then the third and fourth and so on, i.e.(1×2), (2×3), (3×4), . . . , the invention also comprehends using otherneighbor multiplications, such as (1×2) (3×4) (5×6), . . . , or (1×3)(2×4) (3×5) (4×6), . . . (although the first type of neighbormultiplication (i.e. (1×2), (2×3), (3×4), . . . ) is preferred by theinventor.

[0061] It should also be understood that although the above descriptionhas been in terms of constructing a matrix c_(p,m) of correlations forp,m pairs (the matrix given by eq. (7), with values for the real andimaginary components of each element given by eqs. (5) and (6)respectively after demodulation of a signal fragment using the correctcode phase and coarse frequency as explained above), the invention isnot limited to implementations in which all of the matrix elements areheld in a memory device at any one time. In particular, it is usuallypreferable to perform all the integrations for a first p,m pair, thenfor each next such pair, perform the calculations and compare theresults to those for the previous pair and keep only the largest result(of course also keeping note of the p,m pair that gave rise to thecurrent largest result).

SCOPE OF THE INVENTION

[0062] It is to be understood that the above-described arrangements areonly illustrative of the application of the principles of the presentinvention. In particular, it should be noted that the invention is in noway limited to use in a ranging receiver as illustrated in FIG. 2, whichis provided only as an example of a ranging receiver in which theinvention can be implemented; as another example, besides using a NCO towipe off (approximately demodulate) the carrier (by removing a coarsefrequency), discrete Fourier transforms (DFTs) are used. Numerousmodifications and alternative arrangements may be devised by thoseskilled in the art without departing from the spirit and scope of thepresent invention, and the appended claims are intended to cover suchmodifications and arrangements.

What is claimed is:
 1. A method for determining information about thecarrier frequency of a signal transmitted by a possibly movingtransmitter, the signal having a code component and a carrier component,the method comprising: a) a step (100) of responding to successiveapproximately carrier-demodulated received signal fragments (102), andproviding a set (104) of correlation results indicating informationabout the correlation of the approximately carrier-demodulated receivedsignal fragments with a replica of the code component and any remainingcarrier component, wherein the set (104) is formed using differentpossible offsets from a nominal carrier frequency used to approximatelycarrier-demodulate the received signal fragment, and further whereineach element of the set (104) is provided as a phasor (c_(p,m)) having amagnitude and a phase; and b) a step (106) of responding to the set(104) of phasors, selecting the phasor (c_(p,m)) having a magnitudedistinguishing it from all the other elements (c_(p,m)) of the set(104), and determining the phase of the selected phasor.
 2. A method asin claim 1, wherein the set (104) of correlation results is a matrix ofcorrelation results, and further wherein the matrix of correlationresults is spanned by an index (m) indicating an offset from a nominalcarrier frequency and also by an index (p) indicating code phase, andstill further wherein the selected phasor (c_(p,m)) is the phasor havingthe maximum magnitude of all the elements of the set (104).
 3. A methodas in claim 2, wherein the step (100) of providing the matrix ofcorrelation results includes a step (11) of performing a coherentintegration of each of a series of signal fragments, and a step (12) ofperforming a non-coherent integration in which the phasor results of thecoherent integrations are combined without regard to phase.
 4. A methodas in claim 3, wherein the step (12) of performing the non-coherentintegration involves multiplying each element of a matrix of correlationresults provided using a coherent integration of a first signalfragment, by the complex conjugate of a corresponding element for animmediately preceding signal fragment.
 5. A method as in claim 2,wherein in providing the matrix of correlation results as phasor values(c_(p,m)) and in determining the phase of the phasor having the maximummagnitude of all the elements of the matrix, only at most two phasorvalues (c_(p,m)) are held in a memory device at any instant of time, andof the two phasor values, only the phasor value (c_(p,m)) having thelarger magnitude is saved in the memory device before calculating a nextphasor value (c_(p,m)).
 6. An apparatus (23) for determining informationabout the carrier frequency of a signal transmitted by a possibly movingtransmitter, the signal having a code component and a carrier component,the apparatus comprising: a) means (300), responsive to approximatelycarrier-demodulated received signal fragments (302), for providing a set(304) of correlation results indicating information about thecorrelation of the approximately carrier-demodulated received signalfragments with a replica of the code component and any remaining carriercomponent, wherein the set (304) is formed using different possibleoffsets from a nominal carrier frequency used to approximatelycarrier-demodulate the received signal fragment, and further whereineach element of the set (304) is provided as a phasor (c_(p,m)) having aphase and a magnitude; and b) means (306), responsive to the set (304)of phasors (c_(p,m)), for selecting the phasor (c_(p,m)) having amagnitude distinguishing it from all the other elements (c_(p,m)) of theset (304), and determining the phase of the selected phasor (c_(p,m)),and for providing information about the carrier frequency based on thephase of the selected phasor (c_(p,m)).
 7. An apparatus as in claim 6,wherein the set (304) of correlation results is a matrix of correlationresults, and further wherein the matrix of correlation results isspanned by an index (m) indicating an offset from a nominal carrierfrequency and also by an index (p) indicating code phase, and stillfurther wherein the selected phasor (c_(p,m)) is the phasor having themaximum magnitude of all the elements of the set (304).
 8. An apparatusas in claim 7, wherein the means for providing the matrix of correlationresults includes means (31), responsive to a series of signal fragments,for performing a coherent integration of each of the series of signalfragments, and also means (32), responsive to the coherent integrations,for providing a non-coherent integration in which the phasor results ofthe coherent integrations are combined without regard to phase.
 9. Anapparatus as in claim 8, wherein the means (32) for performing thenon-coherent integration multiplies each element of a matrix ofcorrelation results provided using a coherent integration of a firstsignal fragment, by the complex conjugate of a corresponding element foran immediately preceding signal fragment.
 10. An apparatus as in claim7, wherein in providing the matrix of correlation results as phasorvalues (c_(p,m)) and in determining the phase of the phasor having themaximum magnitude of all the elements of the matrix, only at most twophasor values (c_(p,m)) are held in a memory device at any instant oftime, and of the two phasor values, only the phasor value (c_(p,m))having the larger magnitude is saved in the memory device beforecalculating a next phasor value (c_(p,m)).
 11. A system, including: atransmitter for transmitting a signal having a code component and acarrier component, and a ranging receiver for receiving the signal andfor determining information about the carrier frequency of the signal,the ranging receiver characterized in that it comprises: a) means (300),responsive to approximately carrier-demodulated received signalfragments (302), for providing a set (304) of correlation resultsindicating information about the correlation of the approximatelycarrier-demodulated received signal fragments with a replica of the codecomponent and any remaining carrier component, wherein the set (304) isformed using different possible offsets from a nominal carrier frequencyused to approximately carrier-demodulate the received signal fragment,and further wherein each element of the set (304) is provided as aphasor (c_(p,m)) having a phase and a magnitude; and b) means (306),responsive to the matrix (304) of phasors (c_(p,m)), for selecting thephasor (c_(p,m)) having a magnitude distinguishing it from all the otherelements (c_(p,m)) of the set (304), and determining the phase of theselected phasor (c_(p,m)), and for providing information about thecarrier frequency based on the phase of the selected phasor (c_(p,m)).12. The system as in claim 11, further comprising a computing resourceexternal to the ranging receiver, and wherein the apparatus communicatesinformation to the computing facility via a wireless communicationsystem and the computing facility provides at least some of thecomputation needed either to provide the set of correlation results orto select the phasor (c_(p,m)).